The non - archive.org version of the site does not contain source code or examples. This filter is really amazing, and I hope someone can implement it. Be aware that there is also a hq2x and a hq4x, but I am linking to 3x because it contains the most information on how the filter works.

hq2x, hq3x and hq4x all use a 3x3 area around the current pixel to determine the interpolation to use.

Attached is a (hopefully correct) representation of one of the 4 pixels to interpolate on hq2x: the top-left (others should be symmetrical). Note: for hq3x, the symmetry will probably be a bit tricky because the output is odd. And for hq4x, we will probably have to make a symmetry with 2x2 pixels...

So on that picture (hq2x/topleft):

On the left (the 3x3 blocks with the blue gradients) is the chosen interpolation when one of the combination on the right is matched. More blue means a more important coefficient, more white means a less important coefficient. Center pixel is the current one.

On the right is the list of all the different combinations triggering that interpolation. When a pixel is red it means there is a visual difference with the current pixel (center). When present, the green lines link 2 pixels which must have a visual difference (in addition to all the other visual diff conditions represented in red).

In various cases we can observe a common pattern in the combinations. For example for the first interpolation (which actually isn't, we just pick the current pixel), we can distinguish the same pattern with some "optional" differences. The representation could be improved to factorize these combinations and mark the optional diff in a different way. Unfortunately, it's not so easy to factorize because of cases like "exclusive optional differences", or "multiple optional differences only".

It might be possible to also swap the representation, but I'm not sure if that would help.

This picture is generated using ​https://github.com/ubitux/hqx. The repository will continue to evolve while I progress on this. The final goal being of course to try to determine the generic rules triggering these interpolation based on the combinations we observe here.